A301832 G.f. A(x) satisfies: A(x) = 1/(1 - x*A(x)/(1 - x^3*A(x)^3/(1 - x^5*A(x)^5/(1 - x^7*A(x)^7/(1 - ...))))), a continued fraction.
1, 1, 2, 5, 15, 49, 168, 595, 2160, 7998, 30095, 114751, 442402, 1721636, 6753869, 26680262, 106042264, 423750562, 1701476738, 6861334966, 27776206851, 112839216109, 459867381701, 1879624039171, 7703187691979, 31647457638073, 130314986803631, 537730217342715, 2223228743506792
Offset: 0
Keywords
Examples
G.f. A(x) = 1 + x + 2*x^2 + 5*x^3 + 15*x^4 + 49*x^5 + 168*x^6 + 595*x^7 + 2160*x^8 + 7998*x^9 + 30095*x^10 + ...
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..500
- Charles H. Conley and Valentin Ovsienko, Quiddities of polygon dissections and the Conway-Coxeter frieze equation, arXiv:2107.01234 [math.CO], 2021.
Formula
a(n) = [x^n] (Sum_{k>=0} A143951(k)*x^k)^(n+1)/(n + 1).
a(n) ~ c * d^n / n^(3/2), where d = 4.36034166192381738574769007441081546251391... and c = 0.42401561796424536417811444539653002307... - Vaclav Kotesovec, Nov 04 2021